$\frac{x^2+7x+12}{x^2-2x-24}$ Divide $\frac{x+3}{x-6}$
You asked:
Evaluate the expression: \(\frac{\frac{{x}^{2} + 7 x + 12}{{x}^{2} - 2 x - 24}}{\frac{x + 3}{x - 6}}\)
MathBot Answer:
Evaluated
\(\displaystyle \frac{\frac{{x}^{2} + 7 x + 12}{{x}^{2} - 2 x - 24}}{\frac{x + 3}{x - 6}} = \frac{\left(x - 6\right) \left(x^{2} + 7 x + 12\right)}{\left(x + 3\right) \left(x^{2} - 2 x - 24\right)} \)
Expanded
\[\frac{\frac{{x}^{2} + 7 x + 12}{{x}^{2} - 2 x - 24}}{\frac{x + 3}{x - 6}} = \frac{x^{2}}{\frac{x^{3}}{x - 6} + \frac{x^{2}}{x - 6} - \frac{30 x}{x - 6} - \frac{72}{x - 6}} + \frac{7 x}{\frac{x^{3}}{x - 6} + \frac{x^{2}}{x - 6} - \frac{30 x}{x - 6} - \frac{72}{x - 6}} + \frac{12}{\frac{x^{3}}{x - 6} + \frac{x^{2}}{x - 6} - \frac{30 x}{x - 6} - \frac{72}{x - 6}}\]
Factored
\[\frac{\frac{{x}^{2} + 7 x + 12}{{x}^{2} - 2 x - 24}}{\frac{x + 3}{x - 6}} = 1\]